Monitoring electrical activity

ABSTRACT

A method and apparatus for monitoring electrical activity, such as brainwaves, in an animal comprising detecting said activity to produce a corresponding output signal, combining the output signal with a random noise signal to produce a modified signal, and analyzing the modified signal using an autocorrelation technique to detect the relative power density values at a plurality of different frequencies. The random noise signal may be a random number. The autocorrelation technique may involve the Yule-Walker method.

The present invention relates to a method of monitoring electricalactivity in an animal, especially human brain waves, and apparatus forcarrying out the method such as an electroencephalograph.

It has been found that when a person is sedated, but not yetanaesthetised, their brain waves contain a frequency component whichoccurs between 8 and 12 Hz, and is known as the alpha rhythm. Assedation passes to full anaesthesia, the alpha rhythm disappears ontermination of anaesthesia as the person returns to a sedated state, itreappears and then tends to disappear again when the person is fullyawake.

It has been realised that this effect may be used to detect anyundesired transition from anaesthesia to sedation, corresponding to theperson beginning to regain consciousness, for example when a surgicaloperation is taking place. However, the emergence of the alpha rhythm,as anaesthesia passes to sedation, represents a small component in thetotal brain wave spectrum, and it has not proved possible using knownmethods to detect the gradual appearance of the alpha rhythm.

In addition, the occurrence of new frequencies lower than the alpha bandsuch as delta, induced by the anaesthetic agent can be used to detectthe undesirable presence of true anaesthesia if the intention is tomaintain a state of sedation.

Known methods of analysing brain waves via electroencephalographsanalyse the brain wave spectra using Fast Fourier Transforms. However,in detecting a weak frequency component, corresponding to the emergingalpha rhythm or low frequency delta rhythm induced by an anaestheticagent, the use of a Fast Fourier Transform is unsuitable. There are tworeasons for this. Firstly, noise in the brain wave signal is analysed bythe Fast Fourier Transform as corresponding to many weak frequencycomponents. It is thus not easy to distinguish between weak frequencycomponents due to noise, and weak frequency component due to otherreasons, such as the emergence of the new frequencies. Secondly, unlessthe frequency component being detected corresponds to one of thesampling frequencies of the Fast Fourier Transform, the Fast FourierTransform will tend to split a frequency signal into a range of spuriousfrequency components.

The result of these two effects is that the Fast Fourier Transform tendsto mask weak components. Hence, it is unsuitable for detecting theemergence of the alpha rhythm. By the time that the alpha rhythm forexample is sufficiently significant to be detectable by Fast FourierTransform, the person will have passed from anaesthesia to sedation, sothat it is not possible in this way to carry out early detection of thattransition.

Therefore, the present invention seeks to provide an apparatus and amethod, of analysing brain waves which permits these rhythms to bedetected when they are very weak. This then permits an indication of theanaesthesia or sedation level to be determined. However, as will beexplained below, the present invention is not limited to detection ofalpha and lower rhythms and could be used to detect other componentssuch as epileptic spikes in the brain wave signal.

According to the present invention, electrical activity is detected andproduces a corresponding output signal, the output signal is combinedwith a random noise signal to produce a modified signal, and themodified signal is analysed using an autocorrelation technique to detectthe relative power density values at a plurality of differentfrequencies.

Preferably, the autocorrelation technique involves use of theYule-Walker algorithm.

The value of one or more power density values at a frequency orfrequencies corresponding to a specific rhythm such as the alpha ordelta is then compared with the sum of the power density values over awider range of frequencies. The result of this comparison gives ameasure which may be used to detect the emergence of these rhythms. Toexpress this in another way, the relative power density D_(f) at variousfrequency f are derived using Equation 1 below, for a multiplicity offrequencies f. $\begin{matrix}{D_{f} = \frac{1}{\left| {1 + {\sum\limits_{p = 1}^{M}\quad {y_{p}{\exp \left( {{- i} \cdot a \cdot f \cdot p} \right)}}}} \right|^{2}}} & {{Equation}\quad 1}\end{matrix}$

where y_(p) is the pth Yule-Walker coefficient, and a is a constant.

Then, the ratio of the sum of one or more values of D_(f) at or aboutthe frequencies of the particular rhythms are compared with the sum ofthe values of D_(f) over a wider range of values, and the changes inthat ratio may be used to detect the emergence of these rhythms.

In general, the maximum frequency of the wider range will be at leastapproximately double that of the maximum frequencies of the rhythmsunder consideration.

It should be noted that Yule-Walker methods from which the Yule-Walkercoefficients referred to in Equation 1 above are obtained, are a knowntype of frequency analysis method. For a detailed discussion ofYule-Walker methods, reference may be made to the book “Digital SignalProcessing” (second edition) by J G Proakis and D G Manolakis publishedby McMillan publishing company, New York.

The present invention also consists in an electroencephalograph whichmonitors brain waves using the method discussed above, to indicate theemergence of specific rhythms, and also consists in a method ofoperation such as an electroencephalograph.

In order to derive the Yule-Walker coefficients referred to above, thepresent invention further proposes that a series of autocorrelationproducts be derived from the brain wave signals. These autocorrelationproducts may then be used directly, to derive the Yule-Walkercoefficients, but it is preferable that an averaging technique isapplied to them. It would be possible to determine the autocorrelationdirect over a relatively long time period, but it is preferable to use ashorter time period and average over those time periods. The advantageof this is that short bursts of noise are then not carried over from oneperiod to the next. Averaging in this way has the disadvantage ofslowing detection of trends, and therefore there is the need tocompromise between these factors.

In deriving the autocorrelation products, it has been found advantageousto add random linear noise to the brain wave signals. Provided that theamount of random linear noise added is not too great. the reduction inspectral resolution which results is not of practical consequence.However, it has been found that the addition of such random linear noisetends to reduce or prevent the occurrence of occasional rogue results.It is also preferable that any DC components of the brain wave signalsbe removed, to counteract the effect of drift.

In order to carry out the analysis of the brain waves as discussedabove, an electroencephalograph according to the present inventionpreferably converts the brain wave signals to digital signals, to enablethose signals to be analysed by a suitably programmed processor. Theanalysis of the relative power density values may then be used togenerate a suitable display and/or audible signal, and/or a controlsignal for other equipment. In fact, it is preferable that the valuecorresponding to the comparison of relative power densities discussedabove is converted to an index value which is a non-linear function ofthe initial value, to emphasise changes at low values of the specificrhythm.

An embodiment of the present invention to define the occurrence of thealpha rhythm will now be described in detail, by way of example, withreference to the accompanying drawings, in which:

FIG. 1 shows an electroencephalograph being an embodiment of the presentinvention;

FIG. 2 shows part of the electroencephalograph of FIG. 1.

Referring first to FIG. 1, an electroencephalograph amplifier unit 10generates electrical signals corresponding to the brain waves, andpasses those signals to an analogue-to-digital converter 11. Theresulting digital signals are passed to a processor 12, in which theyare processed using a Yule-Walker method, as will be described in moredetail later.

The structure of the amplifier unit 10 is shown in more detail in FIG.2. Electrodes 20, for attachment to a person whose brain waves are to beinvestigated, are connected to an input protection circuitry unit 21which protects other parts of the electroencephalograph from damage dueto high voltage discharge. The input protection circuitry unit 21 mayalso act to protect the person to whom the electrodes 20 are connectedfrom failures within the electroencephalograph. As can be seen from FIG.2, the input protection circuitry unit 21 is also connected to ground,so that it passes differential signals to an amplifier unit 22. Thatamplifier unit removes common mode noise, and produces a single signalfrom the input thereto which is then passed to a gain and filter unit23. The gain and filter unit 23 removes high frequency and DC componentsfrom the signal, and further amplifies the signal before it is passed toan isolation amplifier unit 24. That isolation amplifier unit 24 acts asa isolation barrier between the electroencephalograph amplifier 10 andthe analogue to digital converter 11.

As shown in FIG. 1 the processor 12 is powered from a power supply unit13, which may contain a mains connection and a battery back-up so thatthe power is uninterruptable. The program for controlling the processor12 during operation is stored in a memory unit 14.

Furthermore, as is also shown in FIG. 1, the processor 12 may beconnected to a second electroencephalograph amplifier unit 15, by theanalogue digital converter 11. That second electroencephalographamplifier 15 may have the same structure as shown in FIG. 2. Twoauxiliary inputs 16, 17 may be provided to allow digitisation ofnon-isolated inputs from a CAPNOGRAPH or similar equipment.

FIG. 1 also shows that a signal is passed from the processor 12 to theelectroencephalograph amplifiers 10, 15. This signal is an enablingsignal which is passed via an opto-isolator unit 25 (see FIG. 2) to animpedance checker oscillator 26 of the electroencephalograph amplifier10, 15. The opto-isolator unit 25 thus provides electrical safetyisolation between the processor 12 and the electroencephalographamplifier unit 10, 15, in a similar way to the isolation amplifier unit24. When the impedance checker oscillator 26 is enabled by the signalfrom the processor 12, it outputs a frequency signal of between e.g. 5and 10 Hz which is passed via two operational amplifiers 27, 28 togenerate two signals which are passed via transmission gates 29 torespective resistors R1, R2. The resulting signal may be used to assessthe input impedance of the electrodes 20. It can be seen from FIG. 2that the transmission gates 29 are enabled by the signal from theprocessor 12, which is output from the opto-isolator 25. The processingcarried out by the processor 12 will now be described in more detail.

As was mentioned above, the present invention makes use of a Yule-Walkermethod to derive relative power density values. However, it should benoted that theoretical frequency analysis using such methods normallyassume steady state conditions, which do not apply to brain wavesignals. In fact, the consistent frequencies of such signals are oftenstrongly amplitude modulated. Irregular waxing and waning occurs forsome or all of the frequencies with successive maxima intervals varyingwithin a range of half a second to two seconds. Furthermore, eyemovements of the person to whom the electrodes 20 are connected cancause large irregular voltage excursions, and it has also been foundthat there are other non-periodic components. There may also be lowfrequency or DC drift. Hence, in applying a Yule-Walker method to brainwave signals, it is preferable that the processor 12 makes use ofpractical compromises as discussed below.

In the following discussion, various specific values are used todescribe the analysis method. However, the present invention is notlimited to these specific values.

The processor 12 analyses the signals corresponding to the brain wavesin a series of time periods (epochs). The length of time period need notbe fixed, and indeed an electroencephalograph according to the presentinvention may permit the duration of the epochs to be varied. However,an epoch of about 1.5 s duration has been found to be suitable. Assumingthat the sampling rate of the processor 12 was e.g. 128 Hz, this wouldresult in 192 sample values. This can be generalised, however, to Nsample values per epoch, being:

a₀, a₁, . . . a_(n−1)

It has been found that it is then preferable to add random linear noiseto each of these sampled values, it has been found that if this is notdone, consistent results cannot be ensured. Occasional rogue results maybe detected which are sufficiently different from those of adjacentepochs to cause inaccurate analysis. Although addition of a random valuereduces the spectral resolution that can be obtained, it is possible bysuitable selection of the random value, to reduce the requisite errorwithout the reduction of spectral resolution being of practicalsignificance. The consequence of not adding noise in the form of randomvalues is that the frequencies of interest can become too small incomparison to the totality of the other frequencies to be detected attimes of high input noise or large DC offsets before these can beremoved by averaging. Thus, in this embodiment, a modified sampled valuea′_(k), may be obtained, as follows. $\begin{matrix}{a_{k}^{\prime} = {a_{k} + {{{abs}\left( \frac{a_{\max}}{20000} \right)}\left( {500 - {{random}(1000)}} \right)}}} & {{Equation}\quad 2}\end{matrix}$

In equation 2, a_(max) is the numerically greatest sampled value in theepoch, and “random (1000)” is a random positive integer in the range of0 to 1000. Such a random positive integer may be obtained from apseudo-random program of the processor 12.

There may be a DC component imposed on the brain wave signals, and thisDC component may include a drift component. To remove this effect, theaverage value of a′_(k) over all the n values is subtracted from eachvalue a′_(k) to derive a further modified value a″_(k). This process canbe carried out for each epoch, and it should be noted that the additionof the random value discussed above does not introduce a further bias.

Next, a series of autocorrelation products must be derived. The numberof autocorrelation products that need to be derived depend on the orderof the Yule-Walker method used. Assuming that order is m, m+1autocorrelation products will be derived. In practice, values of mbetween 40 and 50 have been found to give satisfactory results. Then,each autocorrelation product x_(p) is given by equation 3 below:$\begin{matrix}{x_{p} = {\frac{1}{n - p}{\sum\limits_{k = 0}^{n - p - 1}\quad {a_{k}^{''}a_{k + p}^{''}}}}} & {{Equation}\quad 3}\end{matrix}$

In this equation p is the number of the autocorrelation product, varyingbetween 0 and m. The values of x_(p) are then a measure in the timedomain of the periodic components of the brain wave signals.

Although it is then possible to use those autocorrelation products x₀ .. . x_(m) to derive Yule-Walker coefficients, it is preferable first toapply an averaging effect across a plurality of epochs. It has beenfound that computing autocorrelation over short epochs, and thencarrying out an averaging operation, is better than calculating theautocorrelation products directly over longer epochs. Short epochs allowfor drift correction, and short bursts of noise do not carry over. Thus,averaging reduces the effect of irregularities in the brain wavesignals, but slows the detection of trends.

A compromise needs to be found between these factors, and it has beenfound that maintaining a running average, over 12 s is a satisfactorycompromise. If 1.5 s epochs are used, as mentioned above, then averagingis over 8 epochs. Then, a new running average R_(p) is derived from theprevious running average R′_(p) by equation 4 below. $\begin{matrix}{R_{p} = \frac{{7R_{p}^{\prime}} + x_{p}}{8}} & {{Equation}\quad 4}\end{matrix}$

Since the running averages R_(p) of the autocorrelation products aredated for each epoch, they are at any time available for analysis of thebrain wave signals. In order to carry out that analysis, it is necessaryto solve Equation 5 below. $\begin{matrix}{{\begin{bmatrix}R_{0} & R_{1} & \cdots & R_{M - 1} \\R_{1} & R_{0} & \cdots & R_{M - 2} \\\vdots & \vdots & \quad & \vdots \\R_{M - 1} & R_{M - 2} & \cdots & R_{0}\end{bmatrix}\begin{bmatrix}Y_{0} \\Y_{1} \\\vdots \\Y_{M}\end{bmatrix}} = {- \begin{bmatrix}R_{1} \\R_{2} \\\vdots \\R_{M}\end{bmatrix}}} & {{Equation}\quad 5}\end{matrix}$

In equation 5, y₀ to y_(m) are the Yule-Walker coefficients.

Although Equation 5 above can be solved in any satisfactory way, it hasbeen found that the Levinson-Durbin solution algorithm may be used, asthis enables the equation to be solved rapidly.

If the sampling rate is at 128 points per second, as previouslymentioned, the relative power density D_(f) at a frequency f is thengiven by Equation 6 below. $\begin{matrix}{D_{f} = \frac{1}{\left| {1 + {\sum\limits_{p - 1}^{M}\quad {y_{p}{\exp \left( {{- i} \cdot \frac{2\quad \pi \quad f}{64} \cdot p} \right)}}}} \right|^{2}}} & {{Equation}\quad 6}\end{matrix}$

It should be noted that since the analysis that is subsequently used inthis embodiment makes use of ratios, rather than absolute values, thenumerator in the above equation has been set to 1.

It is convenient to evaluate the relative power density values D_(f) atintervals of e.g. a quarter Hz.

Then, a ratio α_(r) can be derived from equation 7. $\begin{matrix}{a_{r} = {\left\{ {\sum\limits_{k = 32}^{48}\quad D_{({k/4})}} \right\}/\left\{ {\sum\limits_{k = 2}^{96}\quad D_{({k/4})}} \right\}}} & {{Equation}\quad 7}\end{matrix}$

On the right hand side of this equation, the numerator represents thesum of the relative power density values within the 8 to 12 Hz frequencyrange in which alpha rhythms occur, whilst the denominator is a sum ofthe relative power density values over a frequency range of 0.5 to 24Hz. Hence, α_(r) gives a measure of the power density within the rangecorresponding to alpha rhythms, relative to a much wider frequency rangeencompassing the range of frequencies corresponding to the alpharhythms. Thus, variations in a_(r) represent variations in the powerpresent in alpha rhythms.

Since the present invention seeks to detect the emergence of a specificrhythms, it is more important to detect change of α_(r), from e.g. 0.02to 0.05 than to detect a change from 0.2 to 0.3. Therefore, in a finalstep, the processor may derive a value α_(i) which is a non linearfunction of α_(r) according to Equation 8.

α_(i) =exp{S. ln(α_(r))}  Equation 8

In Equation 8, S is a sensitivity factor. If S equals 1,α_(i) and α_(r)would be the same. In practice, S equals 0.4 is a suitable value.

Once the processor 12 in FIG. 1 has derived the value α_(i) as discussedabove, that value may be used to control. a display which the operatorof the encephalograph may use to detect the emergence of a rhythm. Forexample as shown in FIG. 1, a signal may be passed to a LED display 30which displays the current value of α_(i). In addition, or as analternative, α_(i) may be presented as a vertical bar on an LCD screen31, to give a graphical indication of variations in that value.Information may also be passed via a printer port 32 either directly toa printer, or to a suitable computer for further analysis. FIG. 1 alsoshows that the processor 12 is connected to a key board 33 which permitsthe operator to control the electroencephalograph, for example to inputparameters such as the duration of each epoch. The processor 12 is alsoconnected to a dram memory 34 which permits some data to be storedwhilst the electroencephalograph is powered up.

It should be noted that calculation of a_(i) requires the solution ofEquation 5. Therefore, that equation could be solved every epoch,enabling the displays 30, 31 to be updated every 1.5 s. In practice,such an updating rate is not essential, and the processing load on theprocessor may be reduced by solving equation 8 e.g. every 3 epochs, togive an update of the displays 30, 31 every 4.5 s.

Furthermore. it can be seen from Equation 7 that suitable selection ofthe ranges of the values k in the numerator and denominator of thatequation will enable the power of other frequency components to beinvestigated. Hence, although the present invention has been developedprimarily to detect alpha rhythms occurring in the 8 to 12 Hz frequencyrange, the present invention may be applied to the analysis of otherfrequency components.

What is claimed is:
 1. A method of monitoring electrical activity in ananimal comprising detecting said activity to produce a correspondingoutput signal, combining the output signal with a random noise signal toproduce a modified signal, and analyzing the modified signal using anautocorrelation technique to detect the relative power density values ata plurality of different frequencies.
 2. A method as claimed in claim 1in which the output signal is sampled at intervals.
 3. A method asclaimed in claim 2 in which the samples a_(k) of the output signal aredigital samples.
 4. A method as claimed in claim 3 in which the randomnoise signal consists in a random number that is added to each samplea_(k).
 5. A method as claimed in claim 4 in which successive samples areaveraged over an epoch and the average a_(k)′ subtracted from eachsample a_(k) to produce a modified sample a_(k)″.
 6. A method as claimedin claim 4 in which the samples a_(k), a_(k)″ are processed to derive anumber of autocorrelation products x_(p), using the Yule-Walker method.7. A method as claimed in claim 6, in which$x_{p} = {\frac{1}{n - p}{\sum\limits_{k = 0}^{n - p - 1}\quad {a_{k}^{''}a_{k + p}^{''}}}}$

where p is the number of the autocorrelation product between 0 and m. 8.A method as claimed in claim 7 in which the autocorrelation products x₀to x_(m) are averaged over successive epochs.
 9. A method as claimed inclaim 8 in which a running average R_(p) of the autocorrelation productsis derived from the averages of successive epochs.
 10. A method asclaimed in claim 8 in which the averaged autocorrelation products areanalysed according to the Yule-Walker equation to derive Yule-Walkercoefficients y_(o)to y_(m).
 11. A method as claimed in claim 10 in whichthe Levinson-Durbin algorithm is used to derive the Yule-Walkercoefficients y₀ to y_(m) from the Yule-Walker equation.
 12. A method asclaimed in claim 10 in which the Yule-Walker coefficients are used toderive the relative power density D_(f) at a frequency f of the outputsignal, where$D_{f} = \frac{1}{\left| {1 + {\sum\limits_{p = 1}^{M}\quad {y_{p}{\exp \left( {{- i} \cdot a \cdot f \cdot p} \right)}}}} \right|^{2}}$


13. A method as claimed in claim 12 in which the relative power densityD_(f) is derived for multiple frequencies of the output signal, and therelative power density D_(f) at one frequency or over a first range offrequencies is compared with the power densities D_(f) over a widerrange of frequencies to detect a change in power density at said onefrequency or first range of frequencies.
 14. A method as claimed inclaim 1 applied to the monitoring of brain waves.
 15. Apparatus formonitoring electrical activity in an animal comprising a detector toproduce an output signal corresponding to the electrical activity, arandom noise generator to produce a random noise signal, and a processorto combine the output signal and random noise signal to produce amodified signal and to analyse the modified signal using anautocorrelation technique to detect the elative power density values ata plurality of different frequencies.
 16. Apparatus as claimed in claim15, in which the processor samples the output signal at intervals. 17.Apparatus as claimed in claim 16 in which the processor samples digitalsamples a_(k) of the output signal.
 18. Apparatus as claimed in claim 17in which the random noise generator produces a random noise signal inthe form of a random number that is added to each sample a_(k). 19.Apparatus as claimed in claim 18 in which the processor averagessuccessive samples over an epoch and subtracts the average a_(k)′ fromeach sample a_(k) to produce a modified sample a_(k)″.
 20. Apparatus asclaimed in claim 18 in which the processor processes samples a_(k),a_(k)″ to derive a number of autocorrelation products x_(p) using theYule-Walker method.
 21. Apparatus as claimed in claim 20, in which$x_{p} = {\frac{1}{n - p}{\sum\limits_{k = 0}^{n - p - 1}\quad {a_{k}^{''}a_{k + p}^{''}}}}$

where p is the number of the autocorrelation product between 0 and m.22. Apparatus as claimed in claim 21 in which the autocorrelationproducts x_(o) to X_(m) are averaged by the processor over successiveepochs.
 23. Apparatus as claimed in claim 22 in which a running averageR_(p) of the autocorrelation products is derived by the processor fromthe averages of successive epochs.
 24. Apparatus as claimed in claim 22in which the averaged autocorrelation products are analysed by theprocessor according to the Yule-Walker equation to derive Yule-Walkercoefficients y_(o) to y_(m).
 25. Apparatus as claimed in claim 24 inwhich the processor uses the Levinson-Durbin algorithm to derive theYule-Walker coefficients y_(o) to y_(m) from the Yule-Walker equation.26. Apparatus as claimed in claim 24 in which the processor uses theYule-Walker coefficients to derive the relative power density D_(f) at afrequency f of the output signal, where$D_{f} = \frac{1}{\left| {1 + {\sum\limits_{p = 1}^{M}\quad {y_{p}{\exp \left( {{- i} \cdot a \cdot f \cdot p} \right)}}}} \right|^{2}}$

and a is a constant and M is the order of the Yule-Walker equation. 27.Apparatus as claimed in claim 26 in which the processor derives therelative power density D_(f) for multiple frequencies of the outputsignal, and compares the relative power density D_(f) at one frequencyor over a first range of frequencies with the power densities D_(f) overa wider range of frequencies to detect a change in power density at saidone frequency or first range of frequencies.
 28. Anelectroencephalograph comprising apparatus as claimed in claim 15.